Chapter 5, Problem 16PT

To determine

To write: The inequality , then to solve and then to verify the solution of given problem.

Answer to Problem 16PT

The inequality is $9x-4\ge 23$ with the solution $x\ge 3$ .

Explanation of Solution

Given information:

Nine times a number decreased by four is at least twenty three.

Calculation:

Let the number is x .

Nine times a number decreased by four is $9x-4$

  $9x-4$ is at least twenty three

Then, the inequality is $9x-4\ge 23$

Solve the inequality

  $\begin{array}{l}9x-4+4\ge 23+4\\ 9x\ge 27\\ x\ge 3\end{array}$

Verify the inequality for $x\ge 3$

  $\begin{array}{l}9(3)-4\ge 23\\ 23\ge 23\text{ true}\\ 9(4)-4\ge 23\\ 32\ge 23\text{ true}\end{array}$

Hence, the inequality is $9x-4\ge 23$ with the solution $x\ge 3$ .